Package dev.nm.stat.regression.linear.glm

Class GeneralizedLinearModel

  • All Implemented Interfaces:
    LinearModel
    public class GeneralizedLinearModel
extends Object
implements LinearModel
    The Generalized Linear Model (GLM) is a flexible generalization of the Ordinary Least Squares regression. GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. In GLM, each outcome of the dependent variables, Y, is assumed to be generated from a particular distribution in the exponential family, a large range of probability distributions that includes the normal, binomial and Poisson distributions, among others. The mean, μ, of the distribution depends on the independent variables, X, through
    E(Y) = μ = g-1(Xβ)
    where E(Y) is the expected value of Y; Xβ is the linear predictor, a linear combination of unknown parameters, β; g is the link function.

    The R equivalent function is glm.

    See Also:
    • Wikipedia: Generalized linear model
    • "P. J. MacCullagh and J. A. Nelder. An algorithm for fitting generalized linear models," in Generalized Linear Models, 2nd ed. pp.40. Section 2.5."

    • Constructor Detail

      • GeneralizedLinearModel

        public GeneralizedLinearModel​(GLMProblem problem,
                              GLMFitting fitting)
        Constructs a GeneralizedLinearModel instance.
        Parameters:
        problem - the generalized linear regression problem to be solved
        fitting - the fitting method, c.f., GLMFitting

      • GeneralizedLinearModel

        public GeneralizedLinearModel​(GLMProblem problem)
        Solves a generalized linear problem using the Iterative Re-weighted Least Squares algorithm.
        Parameters:
        problem - the generalized linear regression problem to be solved
        See Also:
        IWLS

    • Method Detail

      • Ey

        public double Ey​(Vector x)
        Description copied from interface: LinearModel
        Computes the expectation \(E(y(x))\) given an input.
        Specified by:
        Ey in interface LinearModel
        Parameters:
        x - an input
        Returns:
        \(E(y(x))\)

      • beta

        public GLMBeta beta()
        Gets the GLM coefficients estimator, β^.
        Specified by:
        beta in interface LinearModel
        Returns:
        the GLM coefficients estimator, β^

      • residuals

        public GLMResiduals residuals()
        Gets the residual analysis of this GLM regression.
        Specified by:
        residuals in interface LinearModel
        Returns:
        the residual analysis of this GLM regression

      • AIC

        public double AIC()
        Gets the Akaike information criterion (AIC).
        Returns:
        the Akaike information criterion (AIC)